The EPR spectrum temperature dependence of Tl2+(II) paramagnetic centers in Rb2SO4, Cs2SO4 crystals have been investigated. At 100K>T>40K the local symmetry of Tl2+(II) paramagnetic centers is C2. The broadening and doubling of EPR spectrum lines with decreasing of T<40K were observed. The angular dependence of lines positions indicate that two structural nonequivalent positions of Tl2+(II) paramagnetic center exist at T<20K. The measurement of dielectric constant of crystals displayed the absence of phase transition in this temperature range. The transformation of EPR spectrum is explained by motion ofTl2+(II) paramagnetic center between two structural nonequivalent states arising near noncentral positions. Parameters of the potential have been extracted by fitting of the temperature dependence of EPR spectrum. Two nonequivalent states are possible due to large difference between ionic radius of Tl2+(II) and Rb+, Cs+.